Periodic solutions of a discrete two-species competitive model with stage structure

In this paper, we investigate the following discrete periodic stage-structure model. x1(k+1)=x1(k)exp{−a1(k)+b1(k)x2(k)x1(k)},x2(k+1)=x2(k)exp{a2(k)x1(k)x2(k)−b2(k)−c(k)x2(k)−β1(k)x3(k)},x3(k+1)=x3(k)exp{d(k)−e(k)x3(k)−β2(k)x2(k)}.x3(k+1)=x3(k)exp{d(k)−e(k)x3(k)−β2(k)x2(k)}. The sufficient and realistic conditions are obtained for the existence of a positive periodic solution of this system.